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Potential energy

  1. Feb 8, 2015 #1
    1. The problem statement, all variables and given/known data
    The net force on the mass is the central force F(r) = -k(r-a). Find the potential energy U(r).
    a is the spring of natural length and k is spring constant k.

    2. Relevant equations
    -dU/dx = F(x)

    3. The attempt at a solution
    [tex]F(r) = - \frac{ dU }{ dr } implies -k(r-a) = - \frac{ dU }{ dr }[/tex]
    So I did this and then integrating both sides I got
    [tex]\frac{ kr^2 }{ 2} - kar = U(r)[/tex] but this doesn't make much sense when I graph it out, as it gives me a parabola, and I would be expecting a asymptotic type function?
     
  2. jcsd
  3. Feb 8, 2015 #2
    Well think about what happens when r > a and r < a. Both states have potential energy and would therefore be parabolic with the vertex at r = a

    P. S. I can't see your pics because I'm on my phone
     
  4. Feb 8, 2015 #3
    I didn't upload any pics, was just making sure, and yes that makes sense, thank you :)
     
  5. Feb 8, 2015 #4
     
    Last edited: Feb 9, 2015
  6. Feb 8, 2015 #5
    Yes, that's must easier to see! Thank you so much!
     
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